Can I Mix Brands and Models on My Vehicle's Wheels?

I recently upgraded my vehicle with a set of brand new Bridgestone Turanza T001s on the rear, but I'm still running the old Firestone FR-500s on the front. The ride is surprisingly smooth and quiet despite the mix of brands and models. However, I've been wondering if this setup could potentially compromise the overall performance and safety of my vehicle. Are there any Bridgestone experts out there who can advise me on whether mixing brands and models on a single set of wheels is acceptable or not? Would love to get some insights from fellow forum members as well!